Thomas Smith and Sons of Saltley had been established in 1848 in Birmingham. After 1880 they built a range of ordinaries, using various brand names. They also supplied parts for bicycles, railway wrenches and tools, until the 1970's. Not all bicycles with Thomas Smith hubs are made in this factory: they had a broad range of parts that were used by smaller makers in the UK and on the continent.
Ordinaries made by Thomas Smith and Sons carry the brand name 'British Mail' and are typically fitted with 'Badger' cranks. No cotter pin needed, they are pinched around the square axle. They are quite straightforward ordinaries, with only a few special details. The Badger-cranks, of course, and I have never before seen such a spring on the front brake.
The yearbook of H.H. Griffin of 1886 tells us the Badger crank is a novelty. In older books we read about bicycles by Thomas Smith with double ball bearings. The bearings on the three Thomas Smith bicycles on the Sterba site are all past 1885 and all fitted with BSA bearings.
Mr. Sterba presents 3 bicycles by Thomas Smith on his website.